The default Outlook setting for a POP account is to delete messages from the server when they are downloaded on an Outlook account. That's why you no longer see them on the phone once they are downloaded on Outlook. This can be a problem if you check your mail from more than one computer and on your phone. I changed my Outlook accounts to an IMAP account quite a while ago for that reason when my small ISP recommended it to us if we liked to keep mail on the server. However, if you go to your Outlook account and use the help function type in something like "work with POP3 messages on multiple computers" and you will get info about changing your settings on a POP3 account to keep mail on the server. I'd recommend changing to an IMAP account if that is possible.
Here's some info from that help section:
"Note Most ISPs have a size limit on your POP3 mailbox. If you do not remove items from the server, your account will eventually exceed the amount allotted by your ISP, therefore, preventing additional messages from being received and possibly incurring additional charges. For more information, contact your ISP"
It's apparently better for the ISPs to keep the mail on the server as IMAP accounts than POP.